A User's Guide to Spectral Sequences

ISBN-13: 9780521567596 / Angielski / Miękka / 2000 / 578 str.

John McCleary; B. Bollobas; W. Fulton

Opis

Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Recenzje

'… this guide is a treasure trove …'. Niew Archief voor Wiskunde

Spis treści

Part I. Algebra: 1. An informal introduction; 2. What is a spectral sequence?; 3. Tools and examples; Part II. Topology: 4. Topological background; 5. The Leray–Serre spectral sequence I; 6. The Leray–Serre spectral sequence II; 7. The Eilenberg–Moore spectral sequence I; 8. The Eilenberg–Moore spectral sequence II; 9. The Adams spectral sequence; 10. The Bockstein spectral sequence; Part III. Sins of Omission: 11. Spectral sequences in algebra, algebraic geometry and algebraic K-theory; 12. More spectral sequences in topology.